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Radial distribution probability

  1. Feb 11, 2010 #1
    1. The problem statement, all variables and given/known data
    When I'm trying to find the probability of finding an electron within a sphere of a certain radius, do i integrate the radial distribution probability function with respect to r from 0 to infinity? My book says the product of the radial distribution function times dr would give the probability, but I always thought you had to integrate it.


    2. Relevant equations
    n/a just looking for a simple answer to my question... i didnt show the hw problem cos i wanna do it myself i just want this question answered.

    3. The attempt at a solution
    I've attempted the problem, i just integrated and I wanna know if you should integrate.
     
  2. jcsd
  3. Feb 11, 2010 #2

    kuruman

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    Homework Helper
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    The probability of finding the particle in a shell of thickness dr having radius r is

    [tex]dP=|\psi|^2\:4\pi r^2dr[/tex]

    The probability of finding the particle anywhere within a sphere of radius R is

    [tex]P=\int^R_0 |\psi|^2\:4\pi r^2dr[/tex]

    Does this help?
     
  4. Feb 11, 2010 #3
    yes! helps a ton! Thank you.
     
  5. Feb 12, 2010 #4
    Notice that [tex]4\pi r^{2}[/tex] is the area of the surface of a sphere. This factor looks like that because you only have radial distribution, independent of azimuthal direction,
    while if your wavefunction looks like [tex]\psi(r,\theta,\phi)[/tex] things will get a little more complicated, and will involve additional integrations.
     
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